Kevin is $3$ years older than Daniel. Two years ago, Kevin was $4$ times as old as Daniel. How old is Kevin now?
Solution: We can use the given information to write down two equations that describe the ages of Kevin and Daniel. Let Kevin's current age be $k$ and Daniel's current age be $d$. The information in the first sentence can be expressed in the following equation: ${k = d + 3}$ Two years ago, Kevin was $k - 2$ years old, and Daniel was $d - 2$ years old. The information in the second sentence can be expressed in the following equation: ${k - 2 = 4(d - 2)}$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $k$, it might be easiest to solve our first equation for $d$ and substitute it into our second equation. Solving our first equation for $d$, we get: ${d = k - 3}$. Substituting this into our second equation, we get the equation: ${k - 2 = 4(} {(k - 3)}{ - 2)}$ which combines the information about $k$ from both of our original equations. Simplifying the right side of this equation, we get: $k - 2 = 4k - 20$. Solving for $k$, we get: $3 k = 18$. $k = 6$.